Empirical likelihood-based inference in a partially linear model for longitudinal data

Abstract

A partially linear model with longitudinal data is considered, empirical likelihood to inference for the regression coefficients and the baseline function is investigated, the empirical log-likelihood ratios is proven to be asymptotically chi-squared, and the corresponding confidence regions for the parameters of interest are then constructed. Also by the empirical likelihood ratio functions, we can obtain the maximum empirical likelihood estimates of the regression coefficients and the baseline function, and prove the asymptotic normality. The numerical results are conducted to compare the performance of the empirical likelihood and the normal approximation-based method, and a real example is analysed.